Lagrangians Manifesting Color-Kinematics Duality in the NMHV Sector of Yang-Mills

TL;DR

This paper constructs explicit Lagrangians for pure Yang-Mills theory that produce duality-satisfying BCJ numerators at tree level in the NMHV sector, revealing a new approach to understanding color-kinematics duality.

Contribution

It introduces minimal auxiliary-field Lagrangians that generate BCJ numerators, advancing the Lagrangian understanding of color-kinematics duality in Yang-Mills theory.

Findings

Lagrangians with up to three auxiliary field pairs produce BCJ numerators.

Explicit tree-level numerators are obtained in the NMHV sector.

The approach simplifies previous Lagrangian constructions for color-kinematics duality.

Abstract

Scattering amplitudes in Yang-Mills theory are known to exhibit kinematic structures which hint to an underlying kinematic algebra that is dual to the gauge group color algebra. This color-kinematics duality is still poorly understood in terms of conventional Feynman rules, or from a Lagrangian formalism. In this work, we present explicit Lagrangians whose Feynman rules generate duality-satisfying tree-level BCJ numerators, to any multiplicity in the next-to-MHV sector of pure Yang Mills theory. Our Lagrangians make use of at most three pairs of auxiliary fields (2,1,0-forms) -- surprisingly few compared to previous attempts of Lagrangians at low multiplicities. To restrict the Lagrangian freedom it is necessary to make several non-trivial assumptions regarding field content, kinetic terms, and interactions, which we discuss in some detail. Future progress likely hinges on relaxing these assumptions.